Heat the oil in a pan and fry the onions over a low heat for about 15 minutes, until soft but not browned.
Add three-quarters of the red wine to deglaze the pan, and cook until the liquid has evaporated.
Add the sugar, thyme, salt and pepper, and cook for another 5 minutes.
Add the remaining wine and keep cooking and stirring until the liquid has cooked off and the onions are sticky. Set aside.
Cook the burger patties until they're about three-quarters done to your liking, and toast the buttered buns, cut side down.
Lay the brie over the patties and cover them to melt the cheese while they finish cooking. Put a lid on the pan, slide the patties under a hot grill for a minute or two, or give them a quick blast in an air fryer until the cheese melts. Take care not to overcook them.
To build the burgers, place a handful of rocket on each bottom bun, add a brie-topped patty, pile on the onions and finish with the top bun.